You can disable lock screen notifications from the Touch ID & Passcode section of the Settings.[1] The same notifications can be disabled for only selected apps from the Notifications section of the Settings.

Steps

Method1

Disabling All Notifications

1

Open the Settings app.

2

Tap Touch ID & Passcode.

3

Enter your passcode (if prompted).

4

Scroll to the bottom.

5

Tap the Notification View slider to turn it off.

Green indicates the feature is on, grey indicates it is off.

Method2

Disabling Notifications for Certain Apps

1

Open the Settings app.

2

Tap Notifications.

3

Tap an App.

4

Tap the Show on Lock Screen slider to turn it off.

Green indicates the feature is on, grey indicates it is off.

This will only disable Lock screen notifications. Other notification types are controlled by other sliders on the same page.